CBSE Important Questions Class 6 Maths Chapter 5 – Prime Time

Class 6 Maths Chapter 5 Prime Time is part of the new NCERT textbook Ganita Prakash. It teaches students about factors and multiples, prime and composite numbers, common factors, co-prime numbers, and the highest common factor (HCF) and lowest common multiple (LCM). Students also learn simple divisibility rules that tell us, without dividing, whether a number can be divided by 2, 3, 4, 5, 6, 8 or 10.

These CBSE important questions for Class 6 Maths Chapter 5 cover sums of prime numbers, cutting ropes into equal pieces using HCF, arranging books in groups using divisibility rules, co-prime pairs, the HCF and LCM rule, digit sums, and forming the smallest number divisible by 8. Every question has a clear step-by-step answer in simple English, so students can practise on their own, parents can check the working, and teachers can use them for class tests. A free printable PDF of these important questions is also available on this page.

CBSE Important Questions Class 6 Maths Chapter 5 – Prime Time

Prime Time (New NCERT)
Medium
Q.
Who am I?
(a) I am a number less than 40. One of my factors is 7. The sum of my digits is 8.
(b) I am a number less than 100. Two of my factors are 3 and 5. One of my digits is 1 more than the other.
Prime Time (New NCERT)
Medium
Q.
Guna says, "Any two prime numbers are co-prime". Is he right?
Prime Time (New NCERT)
Medium
Q.
Write two numbers whose product is 10000. The two numbers should not have 0 as the units digit.
Prime Time (New NCERT)
Medium
Q.
Which of the following numbers are divisible by all of 2, 4, 5, 8 and 10: 572, 2352, 5600, 6000, 77622160.
Prime Time (New NCERT)
Medium
Q.
The teacher asked if 14560 is divisible by all of 2, 4, 5, 8 and 10. Guna checked for divisibility of 14560 by only two of these numbers and then declared that it was also divisible by all of them. What could those two numbers be?
Prime Time (New NCERT)
Medium
Q.
Find the remainders obtained when each of the following numbers are divided by
(i) 10, (ii) 5, (iii) 2.
78, 99, 173, 572, 980, 1111, 2345
Prime Time (New NCERT)
Medium
Q.
Explore and find out if each statement is always true, sometimes true or never true. You can give examples to support your reasoning.
(a) Sum of two even numbers gives a multiple of 4.
(b) Sum of two odd numbers gives a multiple of 4.
Prime Time (New NCERT)
Medium
Q.
Find the largest and smallest 4-digit numbers that are divisible by 4 and are also palindromes.
Prime Time (New NCERT)
Medium
Q.
2024 is a leap year (as February has 29 days). Leap years occur in the years that are multiples of 4, except for those years that are evenly divisible by 100 but not 400.
(a) From the year you were born till now, which years were leap years?
(b) From the year 2024 till 2099, how many leap years are there?
Prime Time (New NCERT)
Medium
Q.
The first number has prime factorisation 2 × 3 × 7 and the second number has prime factorisation 3 × 7 × 11. Are they co-prime? Does one of them divide the other?
Prime Time (New NCERT)
Medium
Q.
Which of the following pairs of numbers are co-prime?
(a) 18 and 35
(b) 15 and 37
(c) 30 and 415
(d) 17 and 69
(e) 81 and 18
Prime Time (New NCERT)
Medium
Q.
Is the first number divisible by the second? Use prime factorisation.
(a) 225 and 27
(b) 96 and 24
(c) 343 and 17
(d) 999 and 99
Prime Time (New NCERT)
Medium
Q.
Are the following pairs of numbers co-prime? Guess first and then use prime factorisation to verify your answer.
(a) 30 and 45
(b) 57 and 85
(c) 121 and 1331
(d) 343 and 216
Prime Time (New NCERT)
Medium
Q.
What is the smallest number whose prime factorisation has:
(a) three different prime numbers?
(b) four different prime numbers?
Prime Time (New NCERT)
Medium
Q.
Find the prime factorisation of these numbers without multiplying first
(a) 56 × 25
(b) 108 × 75
(c) 1000 × 81
Prime Time (New NCERT)
Medium
Q.
Find three prime numbers, all less than 30, whose product is 1955.
Prime Time (New NCERT)
Medium
Q.
The prime factorisation of a number has one 2, two 3s, and one 11. What is the number?
Prime Time (New NCERT)
Medium
Q.
Find the prime factorisations of the following numbers: 64, 104, 105, 243, 320, 141, 1728, 729, 1024, 1331, 1000.
Prime Time (New NCERT)
Medium
Q.
Make such pictures for the following:
(a) 15 pegs, thread-gap of 10,
(b) 10 pegs, thread-gap of 7
(c) 14 pegs, thread-gap of 6
(d) 8 pegs, thread-gap of 3
Prime Time (New NCERT)
Medium
Q.
A Prime Puzzle.
Fill the grid with prime numbers only so that the product of each row is the number to the right of the row and the product of each column is the number below the column.

CBSE Important Questions Class 6 Maths Chapter 5 – Prime Time

Q1. The sum of two prime numbers is always –
(a) Even
(b) Composite
(c) Both composite and even
(d) None of these

Answer: (d) None of these
If both prime numbers are odd (like 3 and 5), their sum 8 is even and composite.
But 2 is also a prime number, and it is even. If we take 2 + 3 = 5, the sum is odd and prime, not even and not composite.
Since one example breaks the rule, the sum of two prime numbers is not always even or composite. So the answer is none of these.

Q2. Two ropes 16 m and 20 m long are to be cut into small pieces of equal lengths. What will be the maximum length of each piece?
(a) 4 m
(b) 5 m
(c) 7 m
(d) 10 m

Answer: (a) 4 m
We need the highest common factor (HCF) of 16 and 20.
Factors of 16: 1, 2, 4, 8, 16
Factors of 20: 1, 2, 4, 5, 10, 20
Common factors: 1, 2, 4
The highest common factor is 4. So each piece can be at most 4 m long.

Ropes of 16 m and 20 m cut into equal pieces of 4 m

Q3. A librarian has 2,346 books to arrange on shelves. She wants to organise them in different ways:
3.1 Can she arrange them in groups of 6?
3.2 The librarian receives 234 more books. Check if the new total (2,346 + 234) is divisible by 4 using divisibility rules.
3.3 Can she arrange them in groups of 2 (pairs)?

Answer: 3.1 Groups of 6: A number is divisible by 6 if it is divisible by both 2 and 3.
2,346 ends in 6, which is even, so it is divisible by 2.
Sum of its digits = 2 + 3 + 4 + 6 = 15, and 15 is divisible by 3, so 2,346 is divisible by 3.
Since it is divisible by both 2 and 3, it is divisible by 6. Yes, she can arrange them in groups of 6.
3.2 Divisible by 4? New total = 2,346 + 234 = 2,580.
A number is divisible by 4 if the number made by its last two digits is divisible by 4.
Last two digits of 2,580 are 80, and 80 ÷ 4 = 20 exactly. So 2,580 is divisible by 4.
3.3 Groups of 2: A number is divisible by 2 if its last digit is even. The last digit of 2,346 is 6, which is even. Yes, she can arrange the books in pairs.

Divisibility checks for 2,346 and 2,580

Q4. Assertion (A): Among the numbers 2, 4, 6, 8, 10, 12, the pairs that are co-prime are (2,4), (4,6), (6,8), (8,10), (10,12).
Reason (R): Two numbers are co-prime if they share no common factors other than 1.
(a) Both A and R are true and R is the correct explanation of A.
(b) Both A and R are true but R is not the correct explanation of A.
(c) A is true but R is false.
(d) A is false but R is true.

Answer: (d) A is false but R is true.
All the numbers 2, 4, 6, 8, 10 and 12 are even, so every pair taken from them has 2 as a common factor. That means none of these pairs is co-prime, so the Assertion is false.
The Reason gives the correct meaning of co-prime numbers, so it is true.

Q5. Assertion (A): HCF(48, 72) × LCM(48, 72) = 48 × 72
Reason (R): For any two positive integers a and b, HCF(a, b) × LCM(a, b) = a × b.
(a) Both A and R are true and R is the correct explanation of A.
(b) Both A and R are true but R is not the correct explanation of A.
(c) A is true but R is false.
(d) A is false but R is true.

Answer: (a) Both A and R are true and R is the correct explanation of A.
The Reason states a rule that works for any two numbers: HCF × LCM = product of the two numbers.
Putting a = 48 and b = 72 in this rule gives HCF(48, 72) × LCM(48, 72) = 48 × 72, which is exactly the Assertion. So the Reason correctly explains the Assertion.

Q6. Which of the following numbers has a sum of its digits that is divisible by both 2 and 5?
1) 1331
2) 1234
3) 11111
4) 992

Answer: Options 2) and 4) are correct.
1) 1331 → digit sum = 1 + 3 + 3 + 1 = 8. 8 is divisible by 2 but not by 5.
2) 1234 → digit sum = 1 + 2 + 3 + 4 = 10. 10 is divisible by both 2 and 5. ✓
3) 11111 → digit sum = 1 + 1 + 1 + 1 + 1 = 5. 5 is divisible by 5 but not by 2.
4) 992 → digit sum = 9 + 9 + 2 = 20. 20 is divisible by both 2 and 5. ✓

Q7. The least number to be subtracted from 149404 for it to be divisible by 10 is

Answer: A number is divisible by 10 if its ones digit is 0.
The ones digit of 149404 is 4, so it is not divisible by 10.
The nearest smaller number ending in 0 is 149400.
149404 − 149400 = 4
So, the least number to be subtracted is 4.

Q8. Which of the following numbers has 4 as a factor?
(a) 1603334
(b) 1502234
(c) 1602324
(d) 1200014

Answer: (c) 1602324
A number has 4 as a factor if the number made by its last two digits is divisible by 4.
(a) 34 is not divisible by 4.
(b) 34 is not divisible by 4.
(c) 24 ÷ 4 = 6, so it is divisible by 4. ✓
(d) 14 is not divisible by 4.

Q9. Which of the following numbers gives a natural number as a quotient when divided by 8?
(a) 20332
(b) 10632
(c) 222054
(d) 30945

Answer: (b) 10632
We get a natural number as the quotient only when the number is exactly divisible by the divisor.
A number is divisible by 8 if the number made by its last three digits is divisible by 8.
(a) 332 is not divisible by 8.
(b) 632 ÷ 8 = 79, so it is divisible by 8. ✓
(c) 054 is not divisible by 8.
(d) 945 is not divisible by 8.

Q10. The smallest 5-digit number formed by using each of the digits 0, 1, 2, 3, 4 only once that is divisible by 8 is

Answer: A number is divisible by 8 if the number made by its last three digits is divisible by 8.
For the smallest 5-digit number, the first digit cannot be 0, so it must be 1. The next smallest digit, 0, goes in the thousands place. The number so far is 1 0 _ _ _ , and the digits left are 2, 3 and 4.
Checking the arrangements of 2, 3 and 4: 234, 243, 324, 342 and 423 are not divisible by 8, but 432 ÷ 8 = 54.
So, the smallest such number is 10432.

The number 10432 with its last three digits 432 divisible by 8

Related Study Material on Extramarks

Q.1 How many faces, edges and vertices does a cuboid have?

2 faces, 4 edges and 6 vertices

4 faces, 6 edges and 6 vertices

5 faces, 10 edges and 8 vertices

6 faces, 12 edges and 8 vertices

Marks:1

Ans

A cuboid is a three dimensional shape which has 6 faces, 12 edges and 8 vertices.

Q.2 A minute hand of a clock starts from 3 and makes an angle of 180° after some time. The minute hand stops at:

(a) 8

(b) 7

(c) 9

(d) 10

Marks:1

Ans(c) 9


If a minute hand of a clock starts from 3 and make an angle of 180°, then it will stop at 9.

Q.3 In which of the following quadrilaterals, the diagonals intersect each other at 90 degrees?
(a) Rhombus

(b) Trapezium

(c) Rectangle

(d) Parallelogram

Marks:1

Ans

(a) Rhombus

Rhombus

In rhombus, the diagonals intersect each other at 90 degrees.

Q.4 Can a triangle have two obtuse angles ?

Marks:1

Ans

No, because the sum of two obtuse angles is more than 180 and this is not possible in the triangle.

Q.5 State true or false : A reflex angle is less than a straight angle.

Marks:1

Ans

False.

A reflex angle is an angle which is more than 180 and less than 360. Also a straight angle is equal to 180°.

Hence, a reflex angle is larger than a straight angle.

Please register to view this section

Chapter 1 - Knowing Our Numbers

Chapter 2 - Whole Numbers

Chapter 3 - Playing with Numbers

Chapter 4 - Basic Geometrical Ideas

Chapter 6 - Integers

Chapter 7 - Fractions

Chapter 8 - Decimals

Chapter 9 - Data Handling

Chapter 10 - Mensuration

Chapter 11 - Algebra

Chapter 12 - Ratio and Proportion

Chapter 13 - Symmetry

Chapter 14 - Practical Geometry

FAQs (Frequently Asked Questions)

Prime Time is a Class 6 Maths chapter about factors, multiples, prime numbers, composite numbers, co-prime numbers and prime factorisation. It also includes divisibility tests for 2, 4, 5, 8 and 10.

A prime number has exactly two factors, 1 and itself. A composite number has more than two factors.

No, 1 is not a prime number. It has only one factor, so it is neither prime nor composite.

Prime factorisation means writing a number as a product of prime numbers. For example, 84 = 2 × 2 × 3 × 7.

Co-prime numbers have no common factor other than 1. For example, 4 and 9 are co-prime because their only common factor is 1.